1. Field of the Invention
This invention relates to a method for generating signals representing a quadratic curve such as a circle, an ellipse or a parabola, and more particularly to a method for generating quadratic curve signals best suited for use in a CRT display unit or a plotter.
2. Description of Prior Art
Known as a conventional method for generating signals representing a quadratic curve by repeating steps that select a new point from among eight points (x+1, y+1), (x+1, y), (x+1, y-1), (x, y-1), (x-1, y-1), (x-1, y), (x-1, y+1) and (x, y+1) adjacent to a current point (x, y) in a Cartesian coordinates system, is a method disclosed by a paper entitled "Algorithm for drawing ellipses or hyperbolae with a digital plotter" by M. L. V. Pitteway, Computer Journal, Vol. 10, November 1967, pp. 282-289.
This method first selects one octant from among the first octant in which point (x+1, y+1) or (x+1, y) can be selected, the second octant in which point (x+1, y) or (x+1, y-1) can be selected, the third octant in which point (x+1, y-1) or (x, y-1) can be selected, the fourth octant in which point (x, y-1) or (x-1, y-1) can be selected, the fifth octant in which point (x-1, y-1) or (x-1, y) can be selected, the sixth octant in which point (x-1, y) or (x-1, y+1) can be selected, the seventh octant in which point (x-1, y+1) or (x, y+1) can be selected, and the eighth octant in which point (x, y+1) or (x+1, y+1) can be selected. Then, by assuming that selectable points in the selected octant are (X.sub.1, Y.sub.1) and (X.sub.2, Y.sub.2) (e.g., X.sub.1 =x+1, Y.sub.1 =y+1, X.sub.2 =x+1 and Y.sub.2 =y in the first octant), that the equation of the quadratic curve is EQU F(x, y)=ax.sup.2 +bxy+cy.sup.2 +dx+ey+f=0,
and that X.sub.3 =(X.sub.1 +X.sub.2)/2 and Y.sub.3 =(Y.sub.1 +Y.sub.2)/2, either (X.sub.1, Y.sub.1) or (X.sub.2, Y.sub.2) is selected according to the sign of D(x,y)=F(X.sub.3, Y.sub.3). Consequently, the next point is selected whether it be in the region of F (x,y).gtoreq.0 or in the region of F (x,y)&lt;0.
The method described in the above paper requires many parameters, complicated operations, and many operations for changing of parameters when changing the octant. And, it has a problem that it is difficult to be realized on hardware.